Shape optimization of acoustic devices using the Scaled Boundary Finite Element Method

Abstract

In this study, the Scaled Boundary Finite Element Method (SBFEM) was used to perform analyses and evaluate the objective function in shape optimization of devices relying on acoustic wave propagation. Similar to the Boundary Element Method (BEM), the SBFEM requires only the discretization of the boundary of the computational domain. However, unlike BEM, there is no need for a fundamental solution; thus, the SBFEM provides a flexibility similar to that of the Finite Element Method (FEM). The dimension reduction is achieved by representing the solution analytically inside the domain and numerically on the boundary. Consequently, the SBFEM provides a flexible platform for shape optimization and alleviates the re-meshing difficulties encountered in FEM. It was shown that domain boundaries can be optimized with a minimum number of design variables, while the existing accurate transparent boundary conditions effectively eliminate the artificial numerical reflections for a wide range of frequencies.